Periodic envelopes of waves over non-uniform depth

Girish K. Rajan, Saziye Bayram, Diane Marie Henderson

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The envelope of narrow-banded, periodic, surface-gravity waves propagating in one dimension over water of finite, non-uniform depth may be modeled by the Djordjević and Redekopp ["On the development of packets of surface gravity waves moving over an uneven bottom," Z. Angew. Math. Phys. 29, 950-962 (1978)] equation (DRE). Here we find five approximate solutions of the DRE that are in the form of Jacobi-elliptic functions and discuss them within the framework of ocean swell. We find that in all cases, the maximum envelope-amplitude decreases/increases when the wave group propagates on water of decreasing/increasing depth. In the limit of the elliptic modulus approaching one, three of the solutions reduce to the envelope soliton solution. In the limit of the elliptic modulus approaching zero, two of the solutions reduce to an envelope-amplitude that is uniform in an appropriate reference frame.

Original languageEnglish (US)
Article number042106
JournalPhysics of Fluids
Volume28
Issue number4
DOIs
StatePublished - Apr 1 2016

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envelopes
gravity waves
elliptic functions
water
oceans
solitary waves

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

Rajan, Girish K. ; Bayram, Saziye ; Henderson, Diane Marie. / Periodic envelopes of waves over non-uniform depth. In: Physics of Fluids. 2016 ; Vol. 28, No. 4.
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Periodic envelopes of waves over non-uniform depth. / Rajan, Girish K.; Bayram, Saziye; Henderson, Diane Marie.

In: Physics of Fluids, Vol. 28, No. 4, 042106, 01.04.2016.

Research output: Contribution to journalArticle

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